Survey sample size calculator
Work out how many responses you need for a given confidence level and margin of error.
Assumes a simple random sample and the worst-case answer split (p = 0.5), so the figure is the largest any result could need.
- Before population correction (n₀)
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- Trimmed by finite population
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- Invitations to send
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| Margin of error | Responses needed | Relative to ±5% |
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"How many responses do we need?" has an arithmetic answer, and it is smaller than most people guess. Ten thousand customers need 370 responses for a ±5% margin at 95% confidence — not a thousand, and not a fixed percentage of the list.
The calculator runs the standard formula. It works out the infinite-population sample, n₀ = z²·p(1−p)/e², then applies the finite population correction, n = n₀ / (1 + (n₀−1)/N), when you tell it how big the group is. Proportion p is fixed at 0.5, the value that maximises p(1−p) and therefore the sample — so the number you get is the worst case, and no answer split will need more than it.
Two things it deliberately does not do. It cannot tell you how many invitations to send to land those responses unless you supply your own response rate, and it cannot rescue a sample that is not random. A survey answered only by the people who felt strongly is biased at any size, and the margin of error says nothing about that.
The z-score comes from the confidence level
Confidence is expressed as a two-tailed z-score: 1.645 for 90%, 1.96 for 95%, 2.576 for 99%. It enters the formula squared, so although the z-score rises only 31% between 95% and 99%, the sample needed for the same margin rises by about 73% — 385 responses become 664.
Margin of error is in percentage points
±5% means an observed 47% could reasonably be anywhere from 42% to 52% — it is not 5% of 47%. Because e is squared in the denominator, halving the margin quadruples the sample: ±5% needs 385 responses, ±2.5% needs 1,537.
Population size matters far less than expected
The finite population correction pulls the sample down only when n₀ is a meaningful fraction of N. For 10,000 people it trims 385 to 370; for 10 million it changes nothing. Leave the population blank if you do not know it and you get the uncorrected, conservative number.
Nothing is sent anywhere
The arithmetic runs in your browser on page load. No population figure, response rate or result reaches a server, and the page keeps working with the network switched off.
Frequently asked questions
Why is p fixed at 0.5?
Because p(1−p) peaks at 0.5, that choice yields the largest sample any answer split could require — 0.5 gives 0.25, while a 90/10 split gives 0.09 and would need roughly a third as many responses. Since you rarely know the split before running the survey, the worst case is the honest default. Fixing it also means the calculator never quietly under-samples you.
Is this the number of invitations to send?
No — it is the number of completed responses you need. Enter your expected response rate and the tool divides through to show how many invitations that implies, but the rate is your estimate, not ours. Email surveys to a customer list commonly land somewhere in single-digit to low-double-digit percentages, so the invitation count is usually the number that decides whether the survey is feasible.
Does it work for comparing subgroups?
Not directly. The margin of error applies to the whole sample, so a subgroup of 40 respondents carries the margin of a sample of 40, not of the full 370. If you plan to report by region, plan or segment, size each group you want to report on separately and add the results together.
What does it not account for?
Non-response bias, clustered or stratified designs (which need a design effect multiplier), repeated measurement of the same people, and questions with more than two meaningful answers where you care about each option separately. It also assumes a simple random sample — if your respondents self-select, the interval is optimistic no matter how large the sample gets.
Other free tools
- Survey margin of error calculator
Calculate the margin of error achieved by a completed survey sample.
- Survey response rate calculator
Measure delivery, start, completion, response and drop-off rates from a survey funnel.
- NPS calculator
Calculate Net Promoter Score from pasted 0–10 responses, including the full breakdown.
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